# A Problem from Pre-RMO 2012.

**Geometry**Level 3

**PS** is a line segment of length **4** and **O** is the midpoint of **PS**. A semicircular arc is drawn with **PS** as diameter. Let **X** be the midpoint of this arc. **Q** and **R** are points on the arc **PXS** such that **QR** is parallel to **PS** and the semicircular arc drawn with **QR** as diameter is tangent to **PS**. What is the area of the region **QXROQ** bounded by the two semicircular arcs?